{
  "id": "2408.08689",
  "version": "v1",
  "published": "2024-08-16T12:05:20.000Z",
  "updated": "2024-08-16T12:05:20.000Z",
  "title": "The splitting of the de Rham cohomology of soft function algebras is multiplicative",
  "authors": [
    "Igor Baskov"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AT",
    "math.AC"
  ],
  "abstract": "Let $A$ be a real soft function algebra. In arXiv:2208.11431 we have obtained a canonical splitting $\\mathrm{H}^* (\\Omega ^\\bullet _{A|\\mathrm{R}}) \\cong \\mathrm{H} ^* (X,\\mathrm{R})\\oplus \\text{(something)}$ via the canonical maps $\\Lambda_A:\\mathrm{H} ^* (X,\\mathrm{R})\\to\\mathrm{H} ^* (\\Omega ^\\bullet _{A|\\mathrm{R}})$ and $\\Psi_A:\\mathrm{H} ^* (\\Omega ^\\bullet _{A|\\mathrm{R}})\\to\\mathrm{H} ^* (X,\\mathrm{R})$. In this paper we prove that these maps are multiplicative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-16T12:05:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rham cohomology",
      "real soft function algebra",
      "multiplicative",
      "canonical maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}